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User blog:Maxime01/Carnaval Event 2019 : Optimising Tickets on Games
Bienvenue les amis, Aim of this blog article - But de cet article Aujourd'hui nous allons voir comment optimiser les chances de gagner des Florins en utilisant au mieux les Tickets de Tombola parmi les jeux proposés lors de l'événement : 2019 Carnival Event Global Warning : This page presents probabilities which are not a sure prediction. Please consider this as the meteo for the weather, it gives you a trend about how the things may probably happen but you can be more lucky or cursed. The strategy here consists in playing several tickets consecutively. The page details how many Tickets are needed for different scenari and how many Florins could be won with the given probabilities. Introduction Tout d'abord un petit rappel des règles extrait de la page correspondante : Most of the action takes place in the event window. You're playing games at the harbor of Venice by spending your Tickets. You decide which game you want to play. Each game costs only one Ticket to play, and don't worry if you run out, the Carnival provides a new free Ticket every hour within the limit of 11 tickets ! When the limit is reached, the timer stops but you can still win additional Tickets from quests or buy some with diamonds. Enter the event window and select any of the three games to play : the "Hammer", the "Gobelets" or the "Boat Race" game. With the "Hammer" game, you can spend your Ticket on a certain win (100%). You will always get 10 Florins in return. However, you can also take a risk and try your luck in one of the other games, where chances to win are lower, but the potential gain is much greater. With the "Gobelets" game, the probability to win is 15%. The pot contains initially 50 Florins. For each Ticket spent, the pool of Florins rises by 10 Florins. The first person lucky enough to win, will take all the Florins that have accumulated in the meantime. With the "Boat Race" game, the probability to win is 5%. The pot contains initially 100 Florins. For each Ticket spent, the pool of Florins rises by 15 Florins. The first person lucky enough to win, will take all the Florins that have accumulated in the meantime. Comparison between games The consistent method to select the most efficient game highly depends on the number of Tickets available. Since this number is limited, one has to restrict this analysis to possible situations occuring during the game. The bar fills till 11 tickets, then a quest can give 5 tickets, the milestone bonus gives also 20 tickets. Iteration should start from 1, 2, 3, 4, 5, 6, then 11, 16, 21, 26 and 31 (bar + milestone bonus). For each game, one column is dedicated to the net gain in Florins and another column to the probability to win at least once. Iteration probabilites can be easily calculation from this website : https://www.dcode.fr/probabilites-tirage In order to calculate the probability to win at least once by spending n Tickets, The formula is the following : P = 1 - ( 1 - odds)^( n_Tickets) P is the probability ; odds depends on the game and the activation of the double chance option n_Tickets is the total of tickets that you plan to spend to increase your chances of winning For example 16 tickets spent (complete bar + one quest bonus) at the "Gobelets" game with 15% chance to win at each attempt (no double chance). P = 1 - (1 - 0,15)^16 = 1 - (0,85)^16 = 0,926 which represents 92,6 % chance to win at least once. The table below indicates the exact ammount of Florins gained if you win after spending exactly the given number of tickets. The percentage column gives the probability to win at least once by spending this number of Tickets (the ammount can be different). Important remark : Each attempt is independent, it is impossible to predict how many Tickets will be necessary to win and which attempt will be successful. Please note that it is assumed that the pot contains 50 Florins for the "Gobelets" game and 100 Florins for the "Boat Race" game at the begining but of course the pot may contain more Florins. Discussion : How to read the table ? You start from the column at the left. How many Tickets do you have ? Let's say that you have 6 Tickets, what could you do ? Obviously, you can : *Play 6 times the "Hammer" game and win 60 Florins at a 100 % probability. *Play 6 times the "Gobelets" game and may win about 110 Florins at a 62,3 % probability. *Play 6 times the "Gobelets" game with the double chance and may lose about 10 Florins at a 88,2 % probability. *Play 6 times the "Boat Race" game and may win about 175 Florins at a 26,5 % probability. *Play 6 times the "Boat Race" game may with the double chance and win about 70 Florins at a 46,9 % probability. Another example with 31 Tickets : *Play 31 times the "Hammer" game and win 310 Florins at a 100 % probability. *Play 31 times the "Gobelets" game and may win about 360 Florins at a 99,4 % probability (unlikely to occur, you will probably win a smallest amount before) *Play 31 times the "Boat Race" game and may win about 550 Florins at a 79,6 % probability. The double chance is useful only if you run out of tickets after many attemps or if you have enough tickets and the pot is really huge. Example : Three tickets remaining on the "Gobelets" game after 13 times failing or 10 Tickets remaining on the "Boat Race" game after 21 times failing. Discussion : when is the double chance relevant ? First of all a probability threshold must be decided : How much do I want to risk ? Is 50% enough or 80% enough ? Another approch consists in multiplying the percentage of winning with the potential gain (ex : with 11 tickets : 110 Florins with 100 %, 160 Florins with 83,3 % or 265 Florins with 43% probability). When deciding whether or not taking the double chance, the ammount of Florins in the pot must be significant and the Tickets spent must be as minimum possible. The potential reward must be superior than the reward by playing the "Hammer" game, the "Gobelet" game, or the "Boat Race" game without double chance. The following formula applies : Florins_in_Pot > Tickets_to_Spent x ( Double_Chance - Ticket_Value_Diff ) + Starting_Pot Florins_in_Pot is the actual value of the Pot ; Tickets_to_Spent depends on the target probability by playing several Tickets consecutively ; Double_Chance = 20 Florins ; Ticket value is the number of Florins added to the Pot each time you spend a Ticket ( 10 Florins for "Hammer" and "Gobelets" and 15 Florins for the Boat Race ) ; Starting Pot equals 50 Florins for the "Gobelets" and 100 Florins for the "Boat Race") Example : At the "Gobelets" game, you want a 83 % probability, therefore you expect about 5 Tickets. Florins_in_Pot > 5 x ( 20 - (10 - 10)) + 50 = 150 Florins With less than 160 Florins in the Pot for the "Gobelets", the double chance option has a poor yield. Example 2 : The "Boat Race". For a probability of 81,5 % ; you need to spend 16 Tickets with Double_Chance. Florins_in_Pot > 16 x ( 20 - (15 - 10)) + 100 = 340 Florins With less than 355 Florins in the Pot at the "Boat Race", the double chance doesn't worth it unless you want to risk a bit. For the "Gobelets" game, the situation with more that 150 Florins in Pot will rarely occur because of the probabilities (100 % - 83,3 % = 16,7 % see table 11 Tickets spent at the "Gobelets" without Double Chance). If it does, it will surely not last long. For the "Boat Race" it may occur more often to have 355 Florins in the Pot (100 % - 56 % = 44 % with 16 Attempts and no Double Chance). However taking the double chance is always a risk, you are not sure to win because remember that other players play simultaneously but you are sure to lose some Florins. Conclusion : optimising the gains and limiting the risks If you have less than ''' '''10 Tickets in reserve, I suggest to play easy with the "Hammer" game. Between 10 and 25 Tickets, probably the "Gobelets" game is the best choice. More than 25 Tickets (validate the Quest 33 milestone when the bar Tickets is full with 11 Tickets), take the risk for Florins with the "Boat Race". Anyway, avoid to play simultaneously at the same moment with another player which can spoil your tickets (observe whetehr the pot of Florins increases or remains constant). The Double Chance is risky and the benefit is usually too low respect with the cost. Other advice : Remember it is just a game, Remain healthy. Eat at least 5 fruits and vegetables per day, sleep at least 8 hours per day, do some sport and don't eat too much fat, salt or sugar. then everything should be fine. Category:Blog posts